Worth noting that Gastornithidae don't appear right away after K/T, they appear about 2/3 of the way thru the Paleocene. This doesn't appear to be any more of a head start over mammals since bigger herbivores like Coryphodon also appear at that time. But
most of these mammalian herbivores would occupy a different niche than a herbivorous Gastornis (if we presume it to have been on a seed- or nut-crushing diet)

I have always assumed that one of the reasons for the evolution of at least some large flightless birds was lack of competition from mammals. This seems highly likely for moas, elephant-birds, giant flightless Hawaiian geese, large flightless galliforms
on New Caledonia and Fiji, dodos etc. it may be have been less of a factor for large birds on continents, but I wonder if the evolution of large size early giant birds such as Gastornis might have been facilitated by a depauperate mammal fauna after the C-T?

Overall, this study affirms something I've long been saying: That
flight in birds is a burden if they don't need it.

While true, this may be said for just about every trait....brains wold be a burden if we didn't need them (probably a burden anyway).

Flight places a
low ceiling on body mass, which is a disadvantage when processing
large amounts of poor-quality plant fodder.

And yet plenty of volant species do quite well on poor quality plant fodder (e.g., geese). Food processing is undoubtedly a strongly selected trait...but many traits are strongly selected. For large, flightless birds, predation on eggs and juveniles may
well be a stronger target of selection!

Large flightless
herbivores dominate the base of Neornithes - both Palaeognathae and
Galloanserae. One hypothesis is that terrestrial-based volant birds
(including those in continental ecosystems) became better adapted to
evade or defend against terrestrial predators - and over time spent
more time on the ground, and eventually lost the ability to fly.

Predation on adults is apparently not much concern to ostriches...they do suffer intense offspring predation. And in this sense, the bird (and non avian dinosaurian) reproductive imperatives work _against_ large size. This is due to one tyrannical factor:
the bigger the parent, the smaller the offspring. The window for offspring predation is longer than for other reproductive systems...mammals bake babies for longer and they are closer to adult size when born; croc babies escape a good portion of their predators
by hiding in the water. Same for turtle offspring. Others have argued that _small_ size leading to flexibility of nesting sites (e.g., islands, cliffs, trees) helped these species outcompete large species. Indeed, small volant species overwhelm the diversity
of large flightless birds even as there is ample niche space (absent predators) for the large body plan. Niche requirements are critical for all species. But I feel that a paramount element of the large flightless bird niche is missing in most habitats: low
offspring-predator density.

So what was the ecological context to explain the diversity of large flightless birds earlier in the Cenozoic? Better hiding places (including wetlands and grasslands), fewer predators, island life? There has always been low quality fodder and I agree
these birds would have been ferocious adults. But, in light of the current difficulties experienced by this body plan, and its extremely low diversity, I would love to see more research on specific localities.